Most algorithms constructing bases of finite-dimensional vector spaces return basis vectors which, apart from orthogonality, do not show any special properties. While every basis is sufficient to define the vector space, not all bases are equally suited to unravel properties of the problem to be solved. In this paper a normal form for bases of finite-dimensional vector spaces is introduced which may prove very useful in the context of understanding the structure of the problem in which the basis appears in a step towards the solution. This normal form may be viewed as a new normal form for matrices of full column rank.

翻译：构造有限维向量空间基的多数算法所返回的基向量，除了正交性之外，并不显现任何特殊性质。尽管每个基都足以定义向量空间，但并非所有基都同样适合揭示待解问题的内在属性。本文引入一种有限维向量空间基的规范形式，该形式在理解问题结构方面可能具有重要价值——当基作为解题步骤出现时，这种规范形式有助于揭示问题的深层结构。该规范形式可视为满秩列矩阵的一种新规范形式。